Get Y by itself so it' should look like this
5y=2x+7 after then you have divide 5 onto the right side and it should look like
Y=2/5x+7/5
7/10 - 1/4 use common denominators
28/40 - 10/40 = 18/40 = 9/20
Answer:
The load balance
Mw minimizes the total cost
Step-by-step explanation:
<u>Optimizing With Lagrange Multipliers</u>
When a multivariable function f is to be maximized or minimized, the Lagrange multipliers method is a pretty common and easy tool to apply when the restrictions are in the form of equalities.
Consider three generators that can output xi megawatts, with i ranging from 1 to 3. The set of unknown variables is x1, x2, x3.
The cost of each generator is given by the formula

It means the cost for each generator is expanded as



The total cost of production is

Simplifying and rearranging, we have the objective function to minimize:

The restriction can be modeled as a function g(x)=0:

Or

We now construct the auxiliary function


We find all the partial derivatives of f and equate them to 0




Solving for \lambda in the three first equations, we have



Equating them, we find:


Replacing into the restriction (or the fourth derivative)




And also


The load balance
Mw minimizes the total cost
Answer:
0.150 < (Proportion of Sandy's pie) < 0.167
15% < (Percentage of Sandy's pie) < 16.7%
Step-by-step explanation:
Total percentage of pie = 100% or 1
George, Sandy, Carlos, and Michelle all ate a piece of the pie.
George ate a fraction of 0.150
Michelle ate a fraction of (1/6) = 0.167
Carlos ate a fraction of (1/7) = 0.143
The amount of pie left = 1 - 0.15 - (1/6) - (1/7) = 0.5405
And Sandy is known to eat more than two of her friends, but less than one of them.
Of the amount of pie eaten by the first 3 friends, (1/6) is the highest proportion.
Hence, it is evident that Sandy ate more than 0.143 and 0.150 (Carlos and George) but less than Michelle (0.167).
So, mathematically, the possible proportion of cake that Sandy ate is
0.150 < (Proportion of Sandy's pie) < 0.167
Hope this Helps!!!
Answer:
8.9 meters
Step-by-step explanation:
this seems like a problem where you can use the pythagorean theorem:
you know one of the two legs (6m) and the hypotenuse (9m), you must find the other leg
a^2 + 6^2 = 9^2
a^2 + 36 = 81
a^2 = 45
a =
or
·
which simplifies to be 3
or approx. 8.9 meters